Signal-processing systems, in particular amplifiers and optical imaging systems, generally do not function in a linear and error-free manner. The output signal I(x) represented in a space having arbitrary coordinates x is usually the convolution of the input signal O(x) and the transfer function T(x) of the system:I(x)=O(x)T(x)  (1),wherein the operator  stands for the convolution. The transfer function T(x) has great technical significance for the use of the signal-processing system. If this function is known, deconvolution can be applied to I(x) in order to deduce the input signal O(x) and, therefore, the physical measured quantity contained in I(x). In imaging systems, T(x) is also referred to as a point spread function.
The functioning of the entire system is therefore improved if the transfer function T(x) is known. A prominent example thereof is the Hubble telescope, the transfer function of which contained the unavoidable optical aberrations and the effects of a systematic lens error. This transfer function was derived, thereby making it possible to correct the images captured by the telescope, which were initially entirely unusable, and to draw conclusions regarding the type and severity of the lens error. This made it possible to subsequently implement an optical correction on the telescope itself.
In order to arrive at the transfer function T(x), the system is usually acted upon by a known input signal O(x) and this is compared to the output signal I(x). In the case of telescopes, a distant star is often depicted as an object that can be described mathematically as an ideal point source using a delta function. In the case of photographing devices, illuminated pin-hole diaphragms, slit diaphragms, or stripe patterns having a variable stripe separation as the test objects are frequently used as known objects. Noise could be used at the input signal O(x) provided a mean function profile was known.
For the cameras of electron microscopes, one utilizes sharp edges as test structures (R. R. Meyer, A. Kirkland, “The effects of electron and photon scattering on signal and noise transfer properties of scintillators in CCD cameras used for electron detection”, Ultramicroscopy 75, 23-33 (1998); R. R. Meyer, A. I. Kirkland, “Characterisation of the Signal and Noise Transfer of CCD Cameras for Electron Detection”, Microscopy Research and Technique 49, 269-280 (2000); R. R. Meyer, A. I. Kirkland, R. E. Dunin-Borkowski, J. L. Hutchison, “Experimental characterisation of CCD cameras for HREM at 300 kV”, Ultramicroscopy 85, 9-13 (2000)) and noise produced by electrons, the ensemble average of which is known (J. M. Zuo, “Electron Detection Characteristics of a Slow-Scan CCD Camera, Imaging Plates and Film, and Electron Image Restoration”, Microscopy Research and Technique 49, 245-268 (2000); K. Du, K. von Hochmeister, F. Philipp, “Quantitative comparison of image contrast and pattern between experimental and simulated high-resolution transmission electron micrographs”, Ultramicroscopy 107, 281-292 (2007)).
This method fails, disadvantageously, when a known test object and, therefore, a known input signal O(x) are unavailable.
The problem addressed by the invention is therefore that of providing a method for determining the transfer function of a signal-processing system that functions without knowledge of the test object and, therefore, without knowledge of the input signal O(x).